We investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas in the presence of a correlated random field that represents an optical speckle pattern. The density is tuned so that the (noninteracting) Fermi energy is close to the mobility edge of the Anderson localization transition. We employ quantum Monte Carlo simulations to determine various ground-state properties, including the equation of state, the magnetic susceptibility, and the energy of an impurity immersed in a polarized Fermi gas (repulsive polaron). In the weakly interacting limit, the magnetic susceptibility is found to be suppressed by disorder. However, it rapidly increases with the interaction strength, and it diverges at a much weaker interaction strength compared to the clean gas. Both the transition from the paramagnetic phase to the partially ferromagnetic phase, and the one from the partially to the fully ferromagnetic phase, are strongly favored by disorder, indicating a case of order induced by disorder.

The highly controllable ultracold atoms in a one-dimensional (1D) trap provide a new platform for the ultimate simulation of quantum magnetism. In this regard, the Néel antiferromagnetism and the itinerant ferromagnetism are of central importance and great interest. Here we show that these magnetic orders can be achieved in the strongly interacting spin-1/2 trapped Fermi gases with additional $p$-wave interactions. In this strong-coupling limit, the 1D trapped Fermi gas exhibits an effective Heisenberg spin $XXZ$ chain in the anisotropic $p$-wave scattering channels. For a particular $p$-wave attraction or repulsion within the same species of fermionic atoms, the system displays ferromagnetic domains with full spin segregation or the antiferromagnetic spin configuration in the ground state. Such engineered magnetisms are likely to be probed in a quasi-1D trapped Fermi gas of ${}^{40}\mathrm{K}$ atoms with very close $s$-wave and $p$-wave Feshbach resonances.

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.

The generation of tunable laser light in the green to orange spectral range has generally been a deficiency of solid-state lasers. Hence, the formalisms of difference frequency generation (DFG) and optical parametric processes are well known, but the DFG of pulsed solid-state lasers was rarely efficient enough for its use in resonance ionization spectroscopy. Difference frequency generation of high-repetition-rate Ti:sapphire lasers was demonstrated for resonance ionization of sodium by efficiently exciting the well-known $D_1$ and $D_2$ lines in the orange spectral range (both $\approx 589$ nm). In order to prove the applicability of the laser system for its use at resonance ionization laser ion sources of radioactive ion beam facilities, the first ionization potential of Na was remeasured by three-step resonance ionization into Rydberg levels and investigating Rydberg convergences. A result of $E_{\text{IP}}=41449.455{\left(6\right)}_{\text{stat}}{\left(7\right)}_{\text{sys}}{\text{cm}}^{-1}$ was obtained, which is in perfect agreement with the literature value of $E_{\text{IP}}^{\text{lit}}=41449.451\left(2\right){\text{cm}}^{-1}$. A total of 41 level positions for the odd-parity Rydberg series $nf{{}^{2}F}_{5/2,7/2}^o$ for principal quantum numbers of $10\le n\le 60$ were determined experimentally.

We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees of freedom. In the regime where the BO approximation is applicable, imaging of the BO nuclear wave function is demonstrated to be possible through reverse use of the reflection principle, when accounting appropriately for the electronic ionization rate. A qualitative difference between the exact and BO wave functions in the asymptotic region of large electronic distances is shown. Additionally, the behavior of the wave function across the turning line is seen to be reminiscent of light refraction. For weak fields, where the BO approximation does not apply, the weak-field asymptotic theory describes the spectrum accurately.

Nonsequential double-recombination (NSDR) high-order-harmonic generation (HHG) is studied in a molecular model system. We observe a unique molecular two-electron effect with a characteristic cutoff in the HHG spectrum at higher energies than what was previously seen for NSDR HHG in atoms. The effect is corroborated with a classical model where it is found that the effect is sensitive to the molecular potential and originates from same-period emission and recombination (SPEAR) of two electrons. The effect persists for intermediate nuclear distances of $R\gtrsim 8.0$ a.u.

In the presence of an external static magnetic field, an atomic gas becomes optically active, showing magneto-optical rotation. In the saturated regime, the coherences among the excited substates give a nonlinear contribution to the rotation of the light polarization. In contrast with the linear magneto-optical rotation, the nonlinear counterpart is insensitive to Doppler broadening. By varying the temperature of a cold strontium gas, we observe both regimes by driving the $J=0\to J=1$ transition on the intercombination line. For this narrow transition, the sensitivity to the static magnetic field is typically three orders of magnitude larger than for a standard broad alkali-metal transition.

We present a pulsed four-wave mixing scheme via a Rydberg state to create, store, and retrieve collective Rydberg polaritons. The storage medium consists of a gas of thermal Rb atoms confined in a $220-\mu \mathrm{m}$-thick cell, which is heated above room temperature. The experimental sequence consists of a pulsed excitation of Rydberg polaritons via the $D_1$ line, a variable delay or storage time, and a final retrieval pulse via the $D_2$ line. The lifetime of the Rydberg polaritons is around 1.2 ns, almost entirely limited by the excitation bandwidth and the corresponding motional dephasing of the atoms. The presented scheme combined with a tightly confined atomic ensemble is a good candidate for a deterministic single-photon source, as soon as strong interactions in terms of a Rydberg blockade are added.

We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type $I_O$, in an antiferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability $I_O$ to a uniform one ${\mathit{\text{III}}}_O$ occurs at a critical magnetic field. All four types of dynamical instability and the pattern transition are ready to be detected in ${}^{23}\mathrm{Na}$ condensates within the availability of the current experimental techniques.

We examine a bosonic two-leg ladder model subject to a magnetic flux and especially focus on a regime where the lower-energy band has two minima. By using a low-energy field theory approach, we study several issues discussed in the system: the existence of local patterns in density and current, chiral-current reversal, and the effect of a nearest-neighbor interaction along the rung direction. In our formalism, the local patterns are interpreted as a result of breaking of discrete symmetry. The chiral-current reversal occurs through a competition between a current component determined at a commensurate vortex density causing an enlargement of the unit cell and another component, which is proportional to the magnetic-field doping from the corresponding commensurate flux. The nearest-neighbor interaction along the rung direction available with the technique on a synthetic dimension is shown to favor a population-imbalance solution in an experimentally relevant regime.

We explore a way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick up a $\pi$ phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half-skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in good agreement with the numerical results.

We present the results of a detailed analytical study of light scattering by a particle with high refractive index $m+i\kappa$ and low losses ($m\gg 1,0<\kappa \ll 1$) based on the exact Mie solution. We show that there is a dramatic difference in the behavior of the electromagnetic field within the particle (inner problem) and outside it (outer problem). With an increase in $m$ at fixed values of the other parameters, the field within the particle asymptotically converges to a periodic function of $m$. The electric and magnetic type Mie resonances of different orders overlap substantially. It may lead to a giant concentration of the electromagnetic energy within the particle. At the same time, we demonstrate that the solution for the outer problem makes it possible to present each partial scattered wave as a sum of two partitions. One of them corresponds to the $m$-independent wave, scattered by a perfectly reflecting particle and plays the role of a background, while the other is associated with the excitation of a sharply $m$-dependent resonant Mie mode. The interference of the partitions brings about a typical asymmetric Fano profile. The profile is obtained from the exact Mie solution by means of identical transformations without any additional assumptions and/or fitting. It makes it possible to generalize rigorously the Fano theory to the case of finite dissipation. At an increase in $m$ the Fano resonances in the outer problem die out and the scattered field converges to the universal, $m$-independent profile. The behavior of the resonances at a fixed $m$ and varying particle size parameter $\left(x\right)$ is also discussed in detail. The similarities and differences of the two cases (fixed $x$, varying $m$ and fixed $m$, varying $x$) are disclosed. We also show that under certain very general conditions the scattering cross section of a large lossy sphere cannot be smaller than half its geometric cross section, while its absorption cross section cannot exceed three halves of the geometric one. Numerical estimates of most discussed effects for a gallium phosphide particle irradiated by the second harmonic of a Nd:YAG laser are presented as an example. In addition to purely academic interest, the obtained results may be employed to design new highly nonlinear heterogenic nanostructures and other metamaterials.

Electromagnetically induced transparency (EIT) has been realized in atomic systems, but fulfilling the EIT conditions for artificial atoms made from superconducting circuits is a more difficult task. Here we report an experimental observation of the EIT in a tunable three-dimensional transmon by probing the cavity transmission. To fulfill the EIT conditions, we tune the transmon to adjust its damping rates by utilizing the effect of the cavity on the transmon states. From the experimental observations, we clearly identify the EIT and Autler-Townes splitting (ATS) regimes as well as the transition regime in between. Also, the experimental data demonstrate that the threshold ${\mathrm{\Omega }}_{\mathrm{AIC}}$ determined by the Akaike information criterion can describe the EIT-ATS transition better than the threshold ${\mathrm{\Omega }}_{\mathrm{EIT}}$ given by the EIT theory.

We classify and distinguish optically biaxial materials, which can have triclinic, monoclinic or orthorhombic crystal symmetry, by the degeneracy of the indices of refraction of their four singular optical axes (Windungsachsen) in the absorption regime. We provide explicit analytical solutions for angular orientations of the singular optical axes in monoclinic crystals and orthorhombic crystals. As a model material we analyze monoclinic gallia $\left(\beta -{\mathrm{Ga}}_2{\mathrm{O}}_3\right)$ and discuss in detail the dispersion (i.e., the spectral variation of the angular position) of its singular optical axes. For a certain energy range $\left(E\approx 7.23–7.33\mathrm{eV}\right)$ we find quasiuniaxial symmetry. At two energies ($E\approx 8.14\mathrm{eV}$ and $E\approx 8.37\mathrm{eV}$) we find triaxial spectral points for which one regular optical axis and two singular optical axes exist. Concurrently a Stokes analysis of the spectral dependence of the electrical field eigenvectors is made and discussed for various crystal orientations. For a singular optical axis $|S_3|=1$; for the two degenerate singular axes at the triaxial point the Stokes vector is undefined. For a certain energy $\left(E=6.59\mathrm{eV}\right)$, the $\langle 010\rangle$ orientation is close to a singular optical axis, $|S_3|=0.977$. The analysis provided here is prototypical for the treatment of the optical properties of optically biaxial functional materials in the absorption and gain regimes.

Second-harmonic generation (SHG) in the Laue scheme of the dynamical Bragg diffraction in one-dimensional photonic crystal (PhC) is studied. The experiments are performed for partially annealed porous-silicon PhC containing 250 periods of the structure. Our measurements confirm that the phase-matched optical SHG is observed under the Bragg conditions, which is evidenced by a narrow angular and spectral distribution of the diffracted SHG outgoing the PhC. This is confirmed by both the analytical description of the SHG process performed in the two-wave approximation, and by direct calculations of the PhC dispersion curves for the fundamental and SHG wavelengths by the revised plane wave method. Possible types of phase- and quasi-phase-matching realized in the studied PhC under the Laue diffraction scheme are discussed.

We study radiative processes of uniformly accelerated entangled atoms, interacting with an electromagnetic field prepared in the Minkowski vacuum state. We discuss the structure of the rate of variation of the atomic energy for two atoms traveling in different hyperbolic world lines. We identify the contributions of vacuum fluctuations and radiation reaction to the generation of entanglement as well as to the decay of entangled states. Our results resemble the situation in which two inertial atoms are coupled individually to two spatially separated cavities at different temperatures. In addition, for equal accelerations we obtain that one of the maximally entangled antisymmetric Bell state is a decoherence-free state.

The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a “product representation formula” allows the standard Heisenberg uncertainty relation to be derived from a classical uncertainty relation for complex random variables. We show this formula also leads to strong uncertainty relations for unitary operators and underlies an interpretation of weak values as optimal (complex) estimates of quantum observables. Furthermore, we show that two incompatible observables that are weakly and strongly measured in a weak measurement context obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values. Moreover, general tradeoff relations between weak purity, quantum purity, and quantum incompatibility, and also between weak and strong joint probability distributions, are obtained based on products of real and imaginary components of weak values, where these relations quantify the degree to which weak probabilities can take anomalous values in a given context.

In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.

Doubly and triply differential cross sections for the bremsstrahlung emission by high-energy spin-polarized electrons in the field of heavy bare nuclei are calculated within a fully relativistic partial-wave approach at collision energies between 1 and 30 MeV. Investigating ${}^{208}\mathrm{Pb}$ as a test case, it is shown that if the photons are emitted at backward angles, nuclear size effects may play an important role even below 10 MeV. Comparison is made with experimental data on the circular polarization correlations between incoming electron and emitted photon at a collision energy of 3.5 MeV. It is demonstrated that, independent of energy, the plane-wave Born approximation severely underestimates the cross section for heavy targets. Moreover, it gives at most a qualitative prescription of the polarization correlations, except possibly in the forward hemisphere.